Where I live, the local 'home depot' sells small battery-powered thingies that locate any cabling or piping, as long as it is metallic, in a wall. I don't know how they are called at your end, probably something like 'cable finder'...

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That will find AC lines only (due to large radiating magnetic field). It will not find a coax cable with a small video signal or no signal at all.

If you know where one end of the cable is, and you want to find the other end, you can short the end that you do have (connect the centre conductor to the shield). Take your multimeter and check all the coax cables you can find, hopefully one of them will be shorted.

If you have access to one end and the other is more or less floating, you can use the kind of cable tracer used by telephone workers: it is a small device connected between the shorted pair (the coax braid in your case) and the ground (earth, distribution frame, pipe, etc.... ). It sends a powerful and characteristic audio signal which is picked up capacitively by a high impedance receiver. It can detect a cable at up to some tens of centimeters, if there isn't too much obstruction.
LV

If you have access to one end and the other is more or less floating, you can use the kind of cable tracer used by telephone workers: it is a small device connected between the shorted pair (the coax braid in your case) and the ground (earth, distribution frame, pipe, etc.... ). It sends a powerful and characteristic audio signal which is picked up capacitively by a high impedance receiver. It can detect a cable at up to some tens of centimeters, if there isn't too much obstruction.
LV

That could work, thanks.

What I was initially thinking of was a device I used many years ago, where you would place a battery operated probe across the power leads in a junction box, and then walk around with a sniffer and follow the cable. It would work through metal conduits - pretty cool. I was stymied with coax, since it's shielded, but I like your approach. It worked by overlaying a high frequency signal (about 1-2 kHz) over the power line fundamental.

However, in the end, I had some notion of where I buried that cable in the wall, and just removed a 6 foot slice of drywall and found it. More work, but no fancy test gear to go buy.